Vault Of Euclid

Integral of x^2 arctan(x)

Techniques of integration core

\(\int x^2 \tan^{-1} x \, dx\)

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What you need first

the integration by parts formula
derivatives of inverse trigonometric functions
polynomial long division or algebraic manipulation
integration by substitution
the integral of 1/x

What this problem tests

Tests integration by parts with inverse trigonometric functions, followed by algebraic manipulation of the resulting rational integrand.

A standard integration problem found in Calculus II courses, testing the ability to combine integration by parts with rational function integration.

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Reduction Formula for a Rational Function core
Area Under the Curve of ln(x)/x warmup
Integral of x^2 ln(x) warmup

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